bathtub
Like a fool, I managed to chip the bathtub in my apartment – what would my best bet be for repairing this, short of replacing the entire tub?
Long story short, I dropped something in the bathtub because my brain is the size of that a small flea, I understand that I'm not worthy of life, and all of that good stuff.
I think that it's a metal tub with a porcelain coating – could this be fixed with a repair kit? 
You can buy bathtub splash guards such as the ones found here.
You should be able to find similar ones at your local hardware store. Most versions install in seconds, using easy peel and stick adhesive backings. No tools, no mess, and usually no waiting for caulks and/or glues to dry.
Its likely the whole cartridge will need replacement. With it you will get a new handle stem.
This might be a sign to replace the whole unit. If you have a three handle setup, a cover plate will let you upgrade to any single handle style. If you go this route, be sure to get a tub filler spout WITH diverter (the single handle tub/shower valves usually don't have diverters.
Best Answer
Nothing you use to repair the porcelain tub fired frit will be as hard and durable but you can look for two part glass filled epoxy resins to repair the porcelain chip. If you are using the tub right now, any shower, shampoo or conditioner residue MUST be completely removed from the chip area prior to or before filling and leveling the epoxy resin. Alcohol followed by acetone swipes will remove most soap residues quickly.
Finding a good color match may be difficult. Looks like a light Almond Beige on my cheap monitor. There are kitchen and bath installer adhesives that are availabe to the trade that allow a good color match but they are usually big kits with many pigment tubes and designed for bonding many linear feet of stone or man made synthetic countertops and bath liners. Did you save any of the porcelain chip for a color match at the store?
Another problem is leveling the repair adhesive bond after applying it to fill the chip. You want a smooth gloss fill to match the surrounding area gloss and color. If the chip is on the bottom of the tub or shower enclosure, then things are easier than if the chip is on the the side of the tub. For side and vertical wall fills, a layer of clear plastic tape can hold the fill in place until it has polymerized to a non sticky high solids fill. In any case, spot sanding to lower and smooth out the patch would be another additional step after applying the bonding fill agent to the chip. Good luck
If you search on "Porcelain Repair Kit Almond" you will get at least a dozen different kits to choose from. Devcon, Permatex Loctite and many others are name brands for epoxy repair and all should work when the directions are followed. Keep it clean and dry before during and after repair for at least 24 hours. There are also tub restoration paints but avoid those unless you feel like re-spraying a well masked complete shower and or tub interior.